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GATE 2019 CE (CE1) – Question 44

Water and Waste Water Quality and Treatment · Unit processes and operations · 2 marks · Multiple choice

A rectangular sedimentation basin is 32 m long, 8 m wide and 4 m deep, with flow 0.2 m³/s. Particle settling follows Stokes’ law. Particle density is 2.5 g/cm³, water density 1 g/cm³, dynamic viscosity 0.01 g/(cm·s), and g = 980 cm/s². Find removal efficiency for uniform spherical particles of diameter 25 μm.

  1. 51%
  2. 65%
  3. 78%
  4. 100%

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Correct answer: (B) 65%

Explanation

Convert to SI: viscosity 0.001 Pa·s, densities 2500 and 1000 kg/m³, diameter $25\times10^{-6}$ m. Stokes settling speed is $$v_s=\frac{9.8(2500-1000)(25\times10^{-6})^2}{18(0.001)}=0.000510417\ \mathrm{m/s}.$$ Surface overflow rate is $v_o=0.2/(32\times8)=0.00078125$ m/s. Removal is $100v_s/v_o=65.33\%$, closest to **65%, B**.